Multivariate Linear Mixed Model in lme4

Question

I wonder how to fit multivariate linear mixed model with lme4. I fitted univariate linear mixed models with the following code:

library(lme4)
lmer.m1 <- lmer(Y1~A*B+(1|Block)+(1|Block:A), data=Data)
summary(lmer.m1)
anova(lmer.m1)

lmer.m2 <- lmer(Y2~A*B+(1|Block)+(1|Block:A), data=Data)
summary(lmer.m2)
anova(lmer.m2)

I'd like to know how to fit multivariate linear mixed model with lme4. The data is below:

Block A B    Y1    Y2
 1    1 1 135.8 121.6
 1    1 2 149.4 142.5
 1    1 3 155.4 145.0
 1    2 1 105.9 106.6
 1    2 2 112.9 119.2
 1    2 3 121.6 126.7
 2    1 1 121.9 133.5
 2    1 2 136.5 146.1
 2    1 3 145.8 154.0
 2    2 1 102.1 116.0
 2    2 2 112.0 121.3
 2    2 3 114.6 137.3
 3    1 1 133.4 132.4
 3    1 2 139.1 141.8
 3    1 3 157.3 156.1
 3    2 1 101.2  89.0
 3    2 2 109.8 104.6
 3    2 3 111.0 107.7
 4    1 1 124.9 133.4
 4    1 2 140.3 147.7
 4    1 3 147.1 157.7
 4    2 1 110.5  99.1
 4    2 2 117.7 100.9
 4    2 3 129.5 116.2

Thank in advance for your time and cooperation.

Answer 1

This can sometimes be faked satisfactorily in nlme/lme4 by simply reformatting your data like

require(reshape)
Data = melt(data, id.vars=1:3, variable_name='Y')
Data$Y = factor(gsub('Y(.+)', '\\1', Data$Y))

> Data
  Block A B Y value
1     1 1 1 1 135.8
2     1 1 2 1 149.4
3     1 1 3 1 155.4
4     1 2 1 1 105.9
5     1 2 2 1 112.9
6     1 2 3 1 121.6
...

and then including the new variable Y in your linear mixed model.

However, for true Multivariate Generalized Linear Mixed Models (MGLMM), you will probably need the sabreR package or similar. There is also an entire book to accompany the package, Multivariate Generalized Linear Mixed Models Using R. If you have a proxy to a subscribing institution, you might even be able to download it for free from http://www.crcnetbase.com/isbn/9781439813270. I would refer you there for any further advice, as this is a meaty topic and I am very much a novice.